Optical lithography has been widely used in the formation of structures included in integrated circuit (IC) chips. Reductions in the size of structures within IC chips have increased the demands placed upon optical lithography systems.
Many methods have been developed to compensate for the image degradation that occurs when the resolution of optical lithography systems approaches the critical dimensions (CD's) of desired lithographic patterns. Critical dimension (CD) refers to the feature size and spacing between features and feature repeats (pitch) that are required by the design specifications, and that are critical for the proper functioning of the devices on a chip. When the critical dimensions (CDs) of a desired IC pattern approach the resolution of a lithographic system (defined as the smallest dimensions that can be reliably printed by the system), image distortions become a significant problem. Currently, the limited resolution of lithography tools poses a challenge to improvements in IC manufacture. The importance of resolution continues to increase as critical dimensions continue to decrease. In order to make the manufacture of future IC products feasible, lithography tools will be required to achieve adequate image fidelity when the ratio of the minimum CD to resolution of the lithographic system is very low.
As an introduction, the resolution ρ (rho) of an optical lithography system can be described by the equation:ρ=kλ/NAwhere ρ is the is the minimum feature size that can be lithographically printed, NA (numerical aperture) is a measure of the amount of light that can be collected by the lens, λ (lambda) is the wavelength of the light source, and k is a factor unique to a given system. One can understand that the resolution ρ is proportional to the wavelength of the light source, and that the image fidelity is improved as diffracted light is collected by the lens over a wider range of directions (i.e., as NA increases). Although a larger NA permits smaller features to be printed, in practice NA is limited by depth-of-focus requirements, by polarization and thin-film effects, by the finite refractive index of the medium (usually air) at the lens exit, and by limitations in lens design. The factor k accounts for aspects of the lithographic process other than wavelength (λ) or numerical aperture (NA), such as resist properties or the use of enhanced masks. In the prior art, typical k-factor values range from about 0.4 to about 0.7. Because of limitations in reducing wavelength λ or increasing numerical aperture NA, the manufacture of smaller IC features (having smaller CD's) will require reducing the k-factor to, for example, the range 0.3-0.4 or smaller, in order to improve the resolution of the lithographic processes.
Components of one embodiment of a projection lithographic system 520 are illustrated in FIG. 1. In FIG. 1, an illumination source 524 provides radiation that illuminates a mask 526, also known as a reticle 526. The illumination source 524 is typically controlled by an illumination controller 522. The terms “mask” and “reticle” may be used interchangeably. Typically, the reticle 526 includes features that act to diffract the illuminating radiation through a lens 530 which projects an image onto an image plane 532, for example, a semiconductor wafer 550 as a substrate 550. The directional extent of radiation transmitted from the reticle 526 to the lens 530 may be controlled by a pupil 401. The illumination source 524 may be capable of controlling various source parameters such as direction and intensity. The wafer 550 typically includes a photoactive material (known as a resist). When the resist is exposed to the projected image, the developed features in the resist closely conform to the desired pattern of features required for the desired IC circuit and devices.
The pattern of features on the reticle 526 acts as a diffracting structure analogous to a diffraction grating which transmits radiation patterns. These radiation patterns can be conveniently described in terms of a Fourier transform in space based on spacing of the features of the diffraction grating (or reticle 526). The Fourier components of diffracted energy associated with the spatial frequencies of the diffracting structure are known in the art as diffracted orders. For example, the zeroth order is associated with the DC component of the mask Fourier transform, while higher Fourier orders arise from modulated patterns in the mask, and are related to the wavelength of the illuminating radiation and inversely related to the spacing (known as pitch) between repeating diffracting features. When the pitch of features is smaller, the angle of diffraction is larger, so that some higher diffracted orders will be diffracted at angles larger than the numerical aperture (NA) of the lens 530. The system 520 may include other apparatus as appropriate, such as, for example, optical filters.
FIG. 5, discussed further herein in the context of an exemplary embodiment, depicts aspects of pixels 1-40 produced by the source 524. FIG. 5 provides a view of the pupil 401, wherein an illumination pupil 402 is also shown, the illumination pupil 402 being that portion of the pupil 401 that is accessible to the illumination source 524. The illumination pupil 402 is typically a central region of the pupil 401, and may be up to about 0.9 NA.
There is increasing interest in methods to optimize the illumination distributions used in photolithography to provide for these small structures. Exemplary U.S. Patents include U.S. Pat. No. 5,680,588, “Method and System for Optimizing Illumination in an Optical Photolithography Projection Imaging System,” issued to Gortych et al, Oct. 21, 1997; and U.S. Pat. No. 6,563,566, “System and Method for Printing Semiconductor Patterns Using an Optimized Illumination and Reticle” issued to Rosenbluth et al., May 13, 2003.
Other publications in this area include “Illuminator Design For The Printing Of Regular Contact Patterns,” M. Burkhardt, A. Yen, C. Progler, and G. Wells, Microelectronic Engineering 41-42, 1998, p. 91; “The Customized Illumination Aperture Filter for Low k1 Photolithography Process,” T.-S. Gau, R.-G. Liu, C.-K. Chen, C.-M. Lai, F.-J. Liang, and C. C. Hsia, SPIE v.4000—Optical Microlithography XIII, 2000, p. 271; “Optimum Mask and Source Patterns to Print a Given Shape,” A. E. Rosenbluth, S. Bukofsky, C. Fonseca, M. Hibbs, K. Lai, A. Molless, R. N. Singh, and A. K. Wong, Journal of Microlithography, Microfabrication, and Microsystems, Vol. 1, No.1, 2002, p. 13; and, “Illumination Optimization of Periodic Patterns for Maximum Process Window,” R. Socha, M. Eurlings, F. Nowak, and J. Finders, Microelectronic Engineering 61-62, 2002, p. 57.
The publication entitled “Optimum Mask and Source Patterns to Print a Given Shape,” as well as U.S. Pat. Nos. 5,680,588 and 6,563,566, describe methods for mathematically optimizing the illumination distribution (“source”) to obtain the sharpest possible image in focus. However, the publication shows that the sharpness of the focused image does not always correlate with the overall lithographic quality, since a small sacrifice in exposure latitude at best-focus can yield a large increase in depth-of-focus (DOF).
Such complexities in lithographic tradeoffs have long been appreciated outside of the context of numerical optimization. The so-called ED-window (exposure defocus) analysis is a convenient way to assess lithographic quality that takes into account both exposure latitude and depth-of-focus. The integrated area of the ED-window is a useful single-parameter metric for assessing overall image quality. More information in this regard is provided in the publication “Level-Specific Lithography Optimization for 1-Gb DRAM,” A. K. Wong, R. Ferguson, S. Mansfield, A. Molless, D. Samuels, R. Schuster, and A. Thomas, IEEE Transactions on Semiconductor Manufacturing 13, No.1, February 2000, p. 76. It is noted that the integrated ED-window, also referred to as the “integrated process window,” is the integral with respect to focal range Δz of the fractional exposure latitude obtained throughout each focal range.
Solving for a maximal integrated ED-window is problematic. This is because the ED metric involves factors that are conditional, non-linear, and non-differentiable. For example, the exposure latitude attained in a given focal range is locally unaffected by all critical distances (CD) in the pattern, except for a particular CD where the exposure sensitivity is the worst for the pattern. That is, the overall performance of the lithographic process is limited to the performance for the weakest feature. Thus, the ED metric reflects a requirement that all features must be printed within a specified tolerance. Similarly, the exposure latitude attained in the extreme defocused plane of a given focal range is not counted as the final exposure latitude applying in that range. Rather, the quantity that is restrictive is the worst case exposure latitude attained in all of the focal planes within the range. Also, even though image intensity (the reciprocal of exposure) is linear in the source intensity, it is usually only the fractional exposure latitude (a nonlinear quantity) that is considered important, since the absolute dose level can typically be adjusted by changing the exposure time. Finally, the result of integration over the focal range that is used to obtain the final figure of merit (i.e., the integrated ED window) must be truncated at the depth-of-focus range where the exposure latitude first drops to zero. This variable truncation represents another non-linear quantity.
These complications limit the reliability of heuristic methods for optimizing lithographic sources over extended focal ranges. Prior art heuristic methods are described in U.S. Pat. Nos. 5,680,588 and 6,563,566, as well as in the publication entitled “Illumination Optimization of Periodic Patterns for Maximum Process Window.” Some of these methods attempt to optimize the image with respect to focus and exposure by applying the focused-image algorithm in multiple focal planes. One may note that an image which has been optimized across multiple focal planes may still exhibit variation in CD through the depth-of-focus, even though the image has been made sharp in each focal plane. Within the context of the teachings for this prior art, one method of addressing this problem is through the addition of CD constraints across the depth-of-focus. However, such equality or band constraints would predictably require adjustment on an ad-hoc or iteration-by-iteration basis, since the depth-of-focus and exposure latitude tradeoff is highly variable from pattern to pattern, and therefore difficult to predict.
Another prior art heuristic algorithm is introduced in the publication entitled “Illumination Optimization of Periodic Patterns for Maximum Process Window.” In this algorithm, the intensity given to each source point (i.e., each illumination direction) is in one embodiment calculated by forming products of two weighting factors, and then summing these products over all pairs of amplitude diffraction orders that the lens 530 collects from the source direction in question. A first of two weighting factors used is (the absolute value of) the intensity spatial frequency produced by the pair of amplitudes. Thus, weighting provides for preferentially augmenting high spatial frequencies in order to sharpen the image. The second weighting factor is obtained by first calculating the normalized derivative with respect to focus of the particular two-order intensity in question. The weighting factor is then calculated by subtracting from 1 the ratio of the focal slope to the maximum focal slope encountered amongst all source points and image frequencies (so that this weighting factor ranges from 1 to 0). Variations of the method are provided, all of which involve similar weighting heuristics. These heuristics are plausibly designed and have been shown to perform acceptably in certain examples.
However, and as with the other methods discussed above, images improved by heuristic methods are not guaranteed to meet standard lithographic criteria for optimal behavior through the depth-of-focus. For example, lithographic performance is customarily considered to be limited by the quality of the least robust printed feature or CD (i.e., the relevant criterion is whether or not every feature is printed within tolerance; if one feature fails, the successful performance of all other features is effectively irrelevant). Unfortunately, a filtering algorithm that emphasizes features with minimal focus and exposure sensitivity can underemphasize the weakest (and therefore most critical) features in the image. Although adjustments could be introduced on an ad-hoc basis to deal with such limitations, these typically do not directly address the problem. With heuristic algorithms, one must usually expect such difficulties will arise, and performance will typically become less reliable when the heuristic adjustments are made more abstract (i.e., when the adjustments do not directly embody the features of the problem which must be solved). On the other hand, standard general-purpose methods for optimization, though non-heuristic, are based on refinement of an initial starting design, and so are limited by the quality of this initial design (i.e., the. solutions provided are usually no better than the particular local optimum associated with the design used to start optimization). This local optimum is not, in general, the desired global optimum. Some general-purpose optimization methods, for example genetic algorithms, do attempt to search beyond the initial local optimum, but there is no guarantee that they will find the global optimum. This is particularly true when more than a few variables are involved, since the potential search space becomes immense. Heuristic methods in some sense consider the properties of the entire search space, but they do so in an uncertain way, and they also do not guarantee that the globally optimum solution is found.
Despite some inherent weakness, heuristic algorithms can often improve the quality of a lithographic image. However, these algorithms leave room for improvement. For example, one would usually expect source weightings that are chosen by heuristic methods to produce appreciable CD errors; correction of these errors using known techniques (e.g. using an optical proximity correction (OPC) program) will in turn change the behavior of the image, and there is no guarantee that iterated cycles of heuristic source optimization and OPC adjustment will converge to an optimal solution.
Although heuristic algorithms can deliver better lithographic images than earlier techniques, the required adjustments to same are not conducive to routine use. What is needed is a method for illuminating the mask 526 with a source 524 that may be used to optimize the image according to an accepted lithographic criterion, such as maximization of the integrated process window through focus.